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Calculus of Several Variables

  • Textbook
  • © 1987

Overview

Authors:
  1. Serge Lang

    1. Department of Mathematics, Yale University, New Haven, USA

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Part of the book series: Undergraduate Texts in Mathematics (UTM)

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Table of contents (17 chapters)

  1. Front Matter

    Pages i-xii
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  2. Basic Material

    1. Front Matter

      Pages 1-1
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    2. Vectors

      • Serge Lang
      Pages 3-48

    3. Differentiation of Vectors

      • Serge Lang
      Pages 49-65

    4. Functions of Several Variables

      • Serge Lang
      Pages 66-86

    5. The Chain Rule and the Gradient

      • Serge Lang
      Pages 87-120

  3. Maxima, Minima, and Taylor’s Formula

    1. Front Matter

      Pages 121-121
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    2. Maximum and Minimum

      • Serge Lang
      Pages 123-142

    3. Higher Derivatives

      • Serge Lang
      Pages 143-179

  4. Curve Integrals and Double Integrals

    1. Front Matter

      Pages 181-181
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    2. Potential Functions

      • Serge Lang
      Pages 183-205

    3. Curve Integrals

      • Serge Lang
      Pages 206-232

    4. Double Integrals

      • Serge Lang
      Pages 233-268

    5. Green’s Theorem

      • Serge Lang
      Pages 269-290

  5. Triple and Surface Integrals

    1. Front Matter

      Pages 291-291
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    2. Triple Integrals

      • Serge Lang
      Pages 293-317

    3. Surface Integrals

      • Serge Lang
      Pages 318-364

  6. Mappings, Inverse Mappings, and Change of Variables Formula

    1. Front Matter

      Pages 365-365
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    2. Matrices

      • Serge Lang
      Pages 367-384

    3. Linear Mappings

      • Serge Lang
      Pages 385-411
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Keywords

About this book

The present course on calculus of several variables is meant as a text, either for one semester following A First Course in Calculus, or for a year if the calculus sequence is so structured. For a one-semester course, no matter what, one should cover the first four chapters, up to the law of conservation of energy, which provides a beautiful application of the chain rule in a physical context, and ties up the mathematics of this course with standard material from courses on physics. Then there are roughly two possibilities: One is to cover Chapters V and VI on maxima and minima, quadratic forms, critical points, and Taylor's formula. One can then finish with Chapter IX on double integration to round off the one-term course. The other is to go into curve integrals, double integration, and Green's theorem, that is Chapters VII, VIII, IX, and X, §1. This forms a coherent whole.

Authors and Affiliations

  • Department of Mathematics, Yale University, New Haven, USA

    Serge Lang

Bibliographic Information

  • Book Title: Calculus of Several Variables

  • Authors: Serge Lang

  • Series Title: Undergraduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-1068-9

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1987

  • Hardcover ISBN: 978-0-387-96405-8Published: 17 February 1987

  • Softcover ISBN: 978-1-4612-7001-0Published: 17 October 2012

  • eBook ISBN: 978-1-4612-1068-9Published: 06 December 2012

  • Series ISSN: 0172-6056

  • Series E-ISSN: 2197-5604

  • Edition Number: 3

  • Number of Pages: XII, 619

  • Additional Information: Originally published by Addison-Wesley, Reading, 1979

  • Topics: Real Functions

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